Finite Group Databasebeta

← #29577417

Subgroups — #29577417

Order 15616.

534 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454859C211yesmaximal, characteristic
2#21450814C211yesmaximal, characteristic
3#21445808C211yesmaximal, characteristic
4#21444492C211yesmaximal, characteristic, complemented
5#21444490C211yesmaximal, characteristic, complemented
6#21443722C211yesmaximal, characteristic, complemented
7C61×#1303C211yesmaximal, characteristic, complemented
8C2×#14519777C2211yescharacteristic
9C2×#14519765—21no—
10C2×C4×D244C2211yescharacteristic
11#16839841—22no—
12#16839839—22no—
13#16839815C2211yescharacteristic
14#16839786C2211yescharacteristic
15C2×#14519693—21no—
16#16839724—22no—
17#16839689C414yes—
18#16839668—21no—
19#16839619—22no—
20#16839530—21no—
21#16839509—22no—
22#16839507—22no—
23C61×#431C2211yescharacteristic
24C61×#423C2211yescharacteristic
25C4×C4⋊C4×C61C2211yescharacteristic
26C22×Dic122—21no—
27C22×D244D411yescharacteristic
28C22×C4×D61D412yes—
29C2×#11758194—21no—
30C2×#11758189—24no—
31#14519777—21no—
32#14519777—21no—
33#14519777—21no—
34#14519777—21no—
35#14519765—42no—
36#14519765—42no—
37C4×D244—21no—
38C4×D244—21no—
39C4×D244—21no—
40C4×D244—21no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61C2×C412yes—
43C2×C4⋊Dic61D411yescharacteristic
44C2×#11758198—24no—
45C2×#11758198C2×C412yes—
46C4⋊#92418—21no—
47C4⋊#92418—21no—
48C4⋊#92418D412yes—
49#14519693—42no—
50C22⋊#92418—21no—
51#14519689—24no—
52C4×#92418—21no—
53#14519684—24no—
54C2×M16×C61—21no—
55C2×C4⋊C4×C61—21no—
56C2×C42×C61—21no—
57C2×C42×C61C2311yescharacteristic
58C4⋊C8×C61—21no—
59C4⋊C8×C61—21no—
60C4⋊C8×C61D412yes—
61C22⋊C8×C61—21no—
62C4×C8×C61—21no—
63#95×C61C2×C412yes—
64C23×D61C22⋊C412yes—
65C22×C4×C61—22no—
66C22×C4×C61C22×C411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×Dic61—22no—
70C22×Dic61C22⋊C412yes—
71C2×D244—21no—
72C2×D244—21no—
73C2×D244—21no—
74C2×D244—21no—
75C2×D244—21no—
76C2×D244—21no—
77C2×C4×D61—22no—
78C2×C4×D61—22no—
79C2×C4×D61—44no—
80C2×Dic122—41no—
81C2×Dic122—41no—
82C2×Dic122—41no—
83C2×Dic122—41no—
84C2×Dic122—41no—
85C2×Dic122—41no—
86M16×C61—41no—
87M16×C61—41no—
88C2×C8×C61—22no—
89C2×C8×C61—41no—
90C4⋊C4×C61—42no—
91C42×C61—41no—
92C42×C61—41no—
93C42×C61C2×D411yescharacteristic
94C42×C61C2×D411yescharacteristic
95C42×C61#4111yescharacteristic
96C42×C61#4111yescharacteristic
97#11758198—22no—
98#11758198—22no—
99#11758198—48no—
100C4⋊Dic61—21no—
101C4⋊Dic61—21no—
102C4⋊Dic61—22no—
103C4⋊Dic61—22no—
104C4⋊Dic61—41no—
105C4⋊Dic61—41no—
106#11758194—41no—
107#11758194—41no—
108C2×#92418—22no—
109C2×#92418—41no—
110#11758189—84no—
111C23×C61C2×C22⋊C411yescharacteristic
112C22×D61—22no—
113C22×D61—22no—
114C22×D61—22no—
115C22×D61—42no—
116C22×D61—42no—
117C2×C4×C61—22no—
118C2×C4×C61—41no—
119C2×C4×C61—42no—
120C2×C4×C61—42no—
121C2×C4×C61—42no—
122C2×C4×C61C4×D411yescharacteristic
123C2×C4×C61C4×D411yescharacteristic
124C2×C4×C61#12011yescharacteristic
125C2×C4×C61#12111yescharacteristic
126C2×C4×C61#12111yescharacteristic
127C2×C4×C61#12311yescharacteristic
128C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C61#13711yescharacteristic
132C2×Dic61—22no—
133C2×Dic61—42no—
134C2×Dic61—42no—
135C2×Dic61—42no—
136C2×Dic61—42no—
137D244—41no—
138D244—41no—
139D244—41no—
140D244—41no—
141C4×D61—44no—
142C4×D61—82no—
143Dic122—81no—
144Dic122—81no—
145Dic122—81no—
146Dic122—81no—
147C8×C61—42no—
148C8×C61—81no—
149#92418—42no—
150#92418—81no—
151#9401—611nomaximal, Sylow
152C22×C61—21no—
153C22×C61—21no—
154C22×C61#38611yescharacteristic
155C22×C61#41711yescharacteristic
156C22×C61#41811yescharacteristic
157C2×D61—44no—
158C2×D61—42no—
159C2×D61—42no—
160C2×D61—42no—
161C2×D61—82no—
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—21no—
165C4×C61—82no—
166C4×C61#45512yes—
167C4×C61#46811yescharacteristic
168C4×C61#46811yescharacteristic
169C4×C61#46911yescharacteristic
170C4×C61#46911yescharacteristic
171Dic61—42no—
172Dic61—82no—
173#2975—611no—
174#2547—611no—
175#1800—611no—
176#1546—611no—
177#1546—611no—
178#1303—611no—
179#1303D6111yescharacteristic, complemented
180C2×C61—21no—
181C2×C61—21no—
182C2×C61#188511yescharacteristic
183C2×C61#189511yescharacteristic
184C2×C61#191511yescharacteristic
185D61—82no—
186C2×C4⋊Q8—611no—
187C2×#124—1221no—
188C2×C4×D4—611no—
189#436—1222no—
190#436—1222no—
191#431—611no—
192#431C2×D6111yescharacteristic
193#423—611no—
194#423C2×D6111yescharacteristic
195C2×#100—1221no—
196#407—1222no—
197#397—614no—
198#391—1221no—
199#380—1222no—
200C4×C4⋊C4C2×D6111yescharacteristic
201#343—1221no—
202#332—1222no—
203#332—1222no—
204C61#940111yescharacteristic, complemented, Sylow
205C22×Q8—1221no—
206C22×D4—611no—
207C23×C4—612no—
208C2×M16—21no—
209C2×M16—1224no—
210C2×M16—1221no—
211C4⋊Q8—1221no—
212C4⋊Q8—1221no—
213C4⋊Q8—1221no—
214C4⋊Q8—1221no—
215#124—2442no—
216#124—2442no—
217C4×D4—1221no—
218C4×D4—1221no—
219C4×D4—1221no—
220C4×D4—1221no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—611no—
223C2×C4⋊C4—612no—
224C2×C4⋊C4—1221no—
225C2×C22⋊C4—612no—
226C2×C22⋊C4—1224no—
227C2×C42—21no—
228C2×C42C22×D6111yescharacteristic
229C4⋊C8—21no—
230C4⋊C8—21no—
231C4⋊C8—612no—
232C4⋊C8—1221no—
233C4⋊C8—1221no—
234C4⋊C8D24412yes—
235#100—2442no—
236C22⋊C8—21no—
237C22⋊C8—1224no—
238C22⋊C8—1221no—
239C4×C8—21no—
240C4×C8—1221no—
241#95—1224no—
242#95C4×D6112yes—
243C24—612no—
244C2×Q8—2441no—
245C2×Q8—2441no—
246C2×Q8—2441no—
247C2×Q8—2441no—
248C2×Q8—2441no—
249C2×Q8—2441no—
250C2×D4—1221no—
251C2×D4—1221no—
252C2×D4—1221no—
253C2×D4—1221no—
254C2×D4—1221no—
255C2×D4—1221no—
256C22×C4—22no—
257C22×C4—612no—
258C22×C4—1222no—
259C22×C4—1222no—
260C22×C4—1222no—
261C22×C4—2444no—
262C22×C4C2×C4×D6111yescharacteristic
263C22×C4D4×D6111yescharacteristic
264C22×C4D4×D6111yescharacteristic
265M16—41no—
266M16—41no—
267M16—4884no—
268M16—2441no—
269M16—2441no—
270C2×C8—22no—
271C2×C8—41no—
272C2×C8—1222no—
273C2×C8—2441no—
274C4⋊C4—42no—
275C4⋊C4—1221no—
276C4⋊C4—1221no—
277C4⋊C4—1222no—
278C4⋊C4—1222no—
279C4⋊C4—2441no—
280C4⋊C4—2441no—
281C22⋊C4—1222no—
282C22⋊C4—1222no—
283C22⋊C4—2448no—
284C42—41no—
285C42—41no—
286C42C2×D24411yescharacteristic
287C42#1175822211yescharacteristic
288C42D4×D6111yescharacteristic
289C42#1175822611yescharacteristic
290C23—1222no—
291C23—1222no—
292C23—1222no—
293C23—2442no—
294C23—2442no—
295C23C22⋊C4×D6111yescharacteristic
296Q8—4881no—
297Q8—4881no—
298Q8—4881no—
299Q8—4881no—
300D4—2441no—
301D4—2441no—
302D4—2441no—
303D4—2441no—
304C2×C4—22no—
305C2×C4—41no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—1222no—
310C2×C4—4882no—
311C2×C4—2442no—
312C2×C4—2442no—
313C2×C4—2442no—
314C2×C4—2444no—
315C2×C4—2442no—
316C2×C4#1451973911yescharacteristic
317C2×C4C4×D24411yescharacteristic
318C2×C4#1451974711yescharacteristic
319C2×C4#1451975011yescharacteristic
320C2×C4#1451975211yescharacteristic
321C2×C4#1451976211yescharacteristic
322C2×C4#1451980111yescharacteristic
323C2×C4#1451980411yescharacteristic
324C2×C4#1451980411yescharacteristic
325C2×C4#1451980911yescharacteristic
326C8—42no—
327C8—81no—
328C8—4881no—
329C8—2442no—
330C22—21no—
331C22—21no—
332C22—4882no—
333C22—2444no—
334C22—2442no—
335C22—2442no—
336C22—2442no—
337C22#1683964011yescharacteristic
338C22#1683976211yescharacteristic
339C22#1683976511yescharacteristic
340C4—21no—
341C4—21no—
342C4—21no—
343C4—82no—
344C4—4882no—
345C4—2442no—
346C4#1683994112yes—
347C4#1684000911yescharacteristic
348C4#1684001111yescharacteristic
349C4#1684001411yescharacteristic
350C4#1684001611yescharacteristic
351C2—21no—
352C2—21no—
353C2—4882no—
354C2#2144620611yescharacteristic
355C2#2144625611yescharacteristic
356C2#2144637011yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1303C2
socleC22×C61#386
prime radicalC22×D244D4
cosocleC2×C42×C61C23
hypercenter#1303D61
hypocenterC61#9401
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1303

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #21444492C2semidirect
5. #21444490C2semidirect
6. #21443722C2semidirect
7. C61×#1303C2semidirect
179. #1303D61semidirect
204. C61#9401semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214548592
#214508142
#214458082
#214444922
#214444902
#214437222
C61×#13032
#940161